Executive Summary

Our project team is VARS Consulting. NBCUniversal has contracted VARS Consulting to analyze box office performance and make strategic recommendations to assess their company’s financial performance for upcoming theatrical releases. As part of this consulting engagement we analyzed the box office data for both NBC Universal and other production companies and used it to drive key insights. In this report we detail how we have gathered and prepared the necessary information and satisfied the clients request using a multiple linear regression model. Finally, we use the selected model to predict likely box office outcomes.

Summary of Findings

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VARS Consulting: Data Science Process

VARS Consulting utilized the following process for this engagement:
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Data Sourcing

We gathered data from two primary sources:
- Internet Movie Database (IMDB): has information related to movies and television shows such as, cast, budgets, plots, reviews etc.

imdbid	title	plot	rating	imdb_rating	metacritic	dvd_release	production	actors	imdb_votes	poster	director	release_date	runtime	genre	awards	keywords	Budget	Box.Office.Gross
tt0010323	The Cabinet of Dr. Caligari	Hypnotist Dr. Caligari uses a somnambulist, Cesare, to commit murders.	UNRATED	8.1	N/A	15-Oct-97	Rialto Pictures	Werner Krauss, Conrad Veidt, Friedrich Feher, Lil Dagover	42,583	https://images-na.ssl-images-amazon.com/images/M/MV5BMTY1NzIxOTcxM15BMl5BanBnXkFtZTgwMjY0ODgwNzE@._V1_SX300.jpg	Robert Wiene	19-Mar-21	67 min	Fantasy, Horror, Mystery	1 nomination.	expressionism\|somnambulist\|avant-garde\|hypnosis\|fair\|visit\|murder\|asylum\|violence\|opening-a-door\|death\|flashback-within-a-flashback\|costume-horror\|flashback\|gothic\|surrealism\|enigma\|kidnapping\|good-versus-evil\|sleepwalking\|mind-control\|macabre\|carnival\|mannequin\|insanity\|evil-doctor\|diabolical\|madman\|megalomania\|megalomaniac\|tragic-villain\|mad-scientist\|sideshow\|hypnotism\|psychopath\|somnambulism\|psychiatrist\|surprise-ending	$18,000	0
tt0052893	Hiroshima Mon Amour	A French actress filming an anti-war film in Hiroshima has an affair with a married Japanese architect as they share their differing perspectives on war.	NOT RATED	8	N/A	24-Jun-03	Rialto Pictures	Emmanuelle Riva, Eiji Okada, Stella Dassas, Pierre Barbaud	21,154	https://images-na.ssl-images-amazon.com/images/M/MV5BMjMyNDYzMzU5OV5BMl5BanBnXkFtZTgwNTUxNzU4MjE@._V1_SX300.jpg	Alain Resnais	16-May-60	90 min	Drama, Romance	Nominated for 1 Oscar. Another 6 wins & 5 nominations.	memory\|atomic-bomb\|lovers-separation\|impossible-love\|nuclear-bomb\|radiation-victim\|nuclear-radiation\|hiroshima-japan\|post-war\|nuclear-weapons\|peace\|german-soldier\|actress\|japanese-man\|anti-war\|first-love\|oblivion\|japan\|nouvelle-vague\|humanism\|death-of-lover\|separation\|sleepless-night\|voice-over-inner-thoughts\|locked-in-a-cellar\|tragic-love\|traumatic-experience\|20th-birthday\|death-of-loved-one\|death-of-boyfriend\|adulterer\|adulteress\|adulterous-desire\|memorial-park\|war-memorial\|peace-demonstration\|film-in-film\|nevers-france\|two-in-a-shower\|survival\|archive-footage\|museum\|radiation-burn\|radiation-poisoning\|1950s\|1940s\|city-in-title\|three-word-title\|french-new-wave\|obliviousness\|first-person-title\|cult-film\|place-name-in-title\|claim-in-title\|part-documentary\|asian-man-white-woman-relationship\|world-war-two\|nonlinear-timeline\|jump-cut\|flashback\|extramarital-affair\|surrealism\|franco-japanese\|hotel\|hotel-room\|frenchwoman\|interracial-love\|interracial-couple\|interracial-romance\|france	$88,300	0
tt0058898	Alphaville	A U.S. secret agent is sent to the distant space city of Alphaville where he must find a missing person and free the city from its tyrannical ruler.	NOT RATED	7.2	N/A	20-Oct-98	Rialto Pictures	Eddie Constantine, Anna Karina, Akim Tamiroff	17,801	https://images-na.ssl-images-amazon.com/images/M/MV5BMzk2MTlkM2EtNzNhYi00Y2YxLWIwODktNGQ0NDM2ZTgwODJiXkEyXkFqcGdeQXVyNjI5NTk0MzE@._V1_SX300.jpg	Jean-Luc Godard	5-May-65	99 min	Drama, Mystery, Sci-Fi	1 win.	dystopia\|french-new-wave\|satire\|comic-violence\|surrealism\|nouvelle-vague\|avant-garde\|neo-noir\|secret-agent\|lemmy-caution\|future\|dictionary\|conscience\|computer\|alternate-reality\|hard-boiled\|spying\|spy-hero\|spy\|reference-to-james-bond\|eurospy\|espionage\|french-science-fiction\|car-chase\|social-satire\|ford-mustang\|violence\|swimming-pool\|spoof\|sexism\|science-runs-amok\|riddle\|neon\|negative-footage\|mind-control\|mathematical-equation\|gun-violence\|galaxy\|forbidden-speech\|evil-computer\|public-execution\|totalitarianism\|philosophy\|bible\|nudity\|utopia-quest\|dictator\|detective\|metropolis\|artificial-intelligence\|spiral-staircase\|based-on-novel\|character-name-in-title	$220,000	$46,585
tt0074252	Ugly, Dirty and Bad	Four generations of a family live crowded together in a cardboard shantytown shack in the squalor of inner-city Rome. They plan to murder each other with poisoned dinners, arson, etc. The …	N/A	7.9	N/A	1-Nov-16	Compagnia Cinematografica Champion	Nino Manfredi, Maria Luisa Santella, Francesco Anniballi, Maria Bosco	5,705	https://images-na.ssl-images-amazon.com/images/M/MV5BMTEwMzkwMDgxNTdeQTJeQWpwZ15BbWU4MDc3MzM1MzAy._V1_SX300.jpg	Ettore Scola	23-Sep-76	115 min	Comedy, Drama	1 win & 2 nominations.	incest\|failed-murder-attempt\|poisoned-food\|baptism\|planning-a-murder\|woman-in-a-wheelchair\|cantankerous-old-woman\|tv-reporter\|domestic-violence\|woman-with-mustache\|brother-in-law-sister-in-law-sex\|avarice\|cupidity\|dysfunctional-family\|burnt-face\|sexual-promiscuity\|money-roll\|misery\|family-patriarch\|traveling-salesman\|promiscuity\|drunkenness\|greed\|scooter\|nude-model\|nude-photograph\|large-family\|360-degree-pan\|vomiting\|sex\|lumpenproletariat\|consumerism\|dream\|black-comedy\|sea\|pregnancy\|extramarital-affair\|prostitute\|male-prostitute\|crossdresser\|poisoning\|long-take\|rome-italy\|family-relationships\|commedia-all’italiana\|woman-on-top\|slum\|italy\|1970s\|poison\|burlesque\|poverty	$6,590	0
tt0084269	Losing Ground	A comedy-drama about a Black American female philosophy professor and her insensitive, philandering, and flamboyant artist husband who are having a marital crisis. When the wife goes off on…	N/A	6.3	N/A	N/A	Milestone Film & Video	Billie Allen, Gary Bolling, Clarence Branch Jr., Joe Garcia	132	https://images-na.ssl-images-amazon.com/images/M/MV5BMTUwMzQzNDg0MV5BMl5BanBnXkFtZTgwMDgwMDUwODE@._V1_SX300.jpg	Kathleen Collins	1-Jun-82	86 min	Comedy, Drama	N/A	artist\|painter\|marriage\|black-independent-film\|independent-film\|professor\|f-rated\|written-by-director\|title-directed-by-female\|female-director\|swimming-pool\|swimming\|filming\|kissing\|painting\|two-word-title\|black-middle-class\|middle-class\|middle-age-couple\|love-triangle\|philosopher	0	0
tt0085180	L’argent	A forged 500-franc note is cynically passed from person to person and shop to shop, until it falls into the hands of a genuine innocent who doesn’t see it for what it is - which will have …	N/A	7.5	95	24-May-05	Criterion Collection	Christian Patey, Vincent Risterucci, Caroline Lang, Sylvie Van den Elsen	5,607	https://images-na.ssl-images-amazon.com/images/M/MV5BY2RlYTc2ZGUtMGFlNS00ZGUxLWEzODYtYjJhY2RmOWRkYzY4L2ltYWdlXkEyXkFqcGdeQXVyNDQzMDg4Nzk@._V1_SX300.jpg	Robert Bresson	18-May-83	85 min	Crime, Drama	2 wins & 3 nominations.	note\|murder\|solitary-confinement\|robbery\|delivery-man\|camera\|bank-robbery\|money\|pushing\|table\|objectified-woman\|unreliable-employee\|woman-in-bed\|old-woman-murdered\|murdered-in-a-bed\|pretending-to-take-medicine\|wristwatch\|working-class\|wine\|whiskey-bottle\|wheelchair\|wheelbarrow\|wealth\|washing-clothes\|waiter\|vengeance\|valium\|trial\|toy-store\|thief\|theft\|telephone-call\|teenage-boy\|teacher\|suitcase\|subway\|stranger\|sticking-out-one’s-tongue\|stealing\|stakeout\|sorting-mail\|sleeping\|sleeping-in-a-barn\|sister-sister-relationship\|sink\|sidewalk-cafe\|shopkeeper\|shop-window\|serving-ladle\|searching\|scrapbook\|school\|schoolboy\|running\|returned-mail\|return-to-sender\|restaurant\|release-from-prison\|redemption\|reckless-driving\|pursuit\|purse\|punishment\|prisoner\|prison-visitation\|prison-guard\|prison-discharge\|prison-cell\|prison-break\|prison-alarm\|priest\|prank\|policeman\|police-van\|police-station\|police-car\|pitchfork\|pill\|picture-frame\|piano\|piano-teacher\|piano-player\|photographer\|perjury\|passing-note\|pajamas\|pacing\|newspaper\|murderer\|murder-of-family\|mother-son-relationship\|mother-daughter-relationship\|moped\|metro\|mass\|mass-murder\|map\|mail\|magazine\|loan\|lie\|liar\|letter\|letter-censorship\|lawyer\|lantern\|knife\|knees\|key\|judge\|ironing\|invoice\|investigator\|investigation\|imprisonment\|husband-wife-relationship\|hunger\|humiliation\|hotel\|hospital\|helmet\|heart-monitor\|headmaster\|handcuffs\|gun\|gunshot\|guilt\|greed\|getaway-car\|gas\|gas-delivery-man\|garden\|friend\|friendship\|fraud\|france\|forgiveness\|forgery\|footbridge\|food\|following\|floor-polisher\|fleeing\|father-son-relationship\|father-daughter-relationship\|family-relationships\|pretending-to-take-a-pill\|face-slap\|escape\|fired-from-the-job\|elevator\|drink\|drinking\|drain\|dog\|dining-hall\|digging-for-potatoes\|death\|death-of-husband\|death-of-daughter\|darkroom\|custody\|cross\|court\|courtroom\|corruption\|confession\|coffee\|clothes-line\|class\|classroom\|cigarette-smoking\|check\|chase\|charity\|cell-mate\|catholic\|catholic-church\|cash-register\|car-accident\|camera-store\|cafe\|burglary\|burglar-alarm\|broken-glass\|broken-dish\|breaking-and-entering\|bread\|blood\|betrayal\|beating\|bakery\|axe-murder\|arrest\|ambulance\|alarm\|accusation\|accomplice\|suicide-attempt\|sleeping-pills\|photo-shop\|multiple-murder\|master-key\|foreign-language-adaptation\|false-testimony\|chain-reaction\|based-on-short-story\|scam\|ex-convict\|counterfeit\|police\|axe\|prison\|death-of-child\|female-nudity	0	0

The description of these fields is as follows:

variable	description
imdbid	Unique ID used by IMDB to refer to the movie.
title	Title of the movie
plot	Movie plot summary
rating	MPAA appropriate audience rating
imdb_rating	IMBD voters scoring of a movie on a scale from 1-10 (10 being best)
metacritic	Metacritic movie score on a scale of 0-100 (100 being best)
dvd_release	Movie release date on DVD
production	Principal production company
actors	Lead actors
imdb_votes	Total votes from IMDB members.
poster	Movie poster artwork
director	Movie director
release_date	Theatrical release date
runtime	Runtime length of movie in minutes
genre	Genre classification
awards	Academy awards & nominations
keywords	Keywords associated with the movie
Budget	Budget spent on the movie production, marketing, and distribution.
box office gross	Box office gross returns as of 9/21/2017

BoxOfficeMojo.com: a box office reporting website that has budget data for movies. Here we used seasonal box office information.

Season.Start	Season.End	Box.Office.Season	Season.Gross	Season.YoY	Season.Days	Season.Daily.Avg	Season.Movie.Count	Season.Move.Avg.Gross
1/5/07	3/1/07	Winter	890.1	-0.024	58	15.3	70	12.7
3/2/07	5/3/07	Spring	1342.3	-0.002	62	21.7	116	11.6
5/4/07	9/3/07	Summer	4210.5	0.128	122	34.5	218	19.3
9/4/07	11/1/07	Fall	947.9	-0.138	58	16.3	120	7.9
11/2/07	1/4/08	Holiday	2299.9	0.082	60	38.3	107	21.5
1/5/08	3/6/08	Winter	1052.7	0.183	64	16.4	99	10.6

Data Combining

We created Excel formulas to identify the season that each release date belonged to so that we could have a master dataset to work with. This final master dataset looked like this:

imdbid	title	plot	rating	imdb_rating	metacritic	dvd_release	production	actors	imdb_votes	poster	director	release_date	runtime	genre	awards	Budget	Box.Office.Gross	Box.Office.Season	Season.Gross	Season.YoY.Change	Season.Days	Season.Daily.Avg	Season.Movie.Count	Season.Movie.Avg	keywords
tt0200465	The Bank Job	Martine offers Terry a lead on a foolproof bank hit on London’s Baker Street. She targets a roomful of safe deposit boxes worth millions in cash and jewelry. But Terry and his crew don’t realize the boxes also contain a treasure trove of dirty secrets - secrets that will thrust them into a deadly web of corruption and illicit scandal.	R	7.3	69	15-Jul-08	Lionsgate	Jason Statham, Saffron Burrows, Stephen Campbell Moore, Daniel Mays	158,562	https://images-na.ssl-images-amazon.com/images/M/MV5BMTUwMzc1MDMxOV5BMl5BanBnXkFtZTcwODY4OTIzMw@@._V1_SX300.jpg	Roger Donaldson	7-Mar-08	111 min	Crime, Drama, Romance	3 nominations.	20000000	30028592	Spring	1074900000	-0.20	55	19543636	111	9700000	safe-deposit\|heist\|chase\|mobster\|london-england\|bank\|pornographer\|blackmail\|secret-service\|bank-vault\|crooked-policeman\|heist-movie\|bank-heist\|walkie-talkie\|torture\|robbery\|tunnel\|murder\|car-dealer\|brothel\|airport\|train-station\|revolver\|weapon\|ford-transit\|ford\|van\|car-salesman\|based-on-true-events\|woman\|20th-century\|england\|united-kingdom\|champagne\|red-wine\|beer\|female-frontal-nudity\|gunfight\|shootout\|fistfight\|sex-scene\|kissing-while-having-sex\|kiss\|neo-noir\|violence\|incriminating-photograph\|s&m\|casual-sex\|black-activist\|paparazzi\|year-1971\|period-piece\|dutch-angle\|debt\|peace-sign\|masochism\|doublecross\|extortion\|recruiting\|planning\|stripper\|caper\|mafia\|suffocation\|strangulation\|stabbed-in-the-back\|pistol\|double-cross\|death\|window-smashing\|what-happened-to-epilogue\|wedding-reception\|vulgarity\|trinidad\|tailor\|subway\|strip-club\|stabbing\|shot-in-the-head\|rooftop\|revolutionary\|railway-station\|pub\|prologue\|princess\|pornographic-film\|political-corruption\|police-corruption\|photograph\|parking-garage\|open-grave\|nonlinear-timeline\|menage-a-trois\|marriage\|machete\|jackhammer\|infidelity\|hidden-camera\|ham-radio\|fishing-boat\|female-nudity\|fashion-model\|drug-smuggling\|customs\|courtroom\|caribbean\|cabinet-officer\|brick\|bracelet\|book-party\|beach\|basement\|assault\|ambulance\|1970s\|dominatrix\|death-of-friend\|based-on-true-story
tt0315642	Wazir	A grief-stricken cop and an amputee grandmaster are brought together by a peculiar twist of fate as part of a wider conspiracy that has darkened their lives.	N/A	7.2	N/A	N/A	Rajkumar Hirani Films	Amitabh Bachchan, Farhan Akhtar, Aditi Rao Hydari, Manav Kaul	12,764	https://images-na.ssl-images-amazon.com/images/M/MV5BMTUzNDU4NDMyOV5BMl5BanBnXkFtZTgwNjcyNzU0NzE@._V1_SX300.jpg	Bejoy Nambiar	8-Jan-16	103 min	Action, Crime, Drama	1 nomination.	586028	0	Winter	1144900000	0.02	59	19405085	86	13300000	chess-grandmaster\|chess\|race-against-time\|one-word-title\|character-name-in-title
tt0323808	The Wicker Tree	Charmed by the residents of Tressock, Scotland, two young missionaries accept the invitation to participate in a local festival, fully unaware of the consequences of their decision.	R	3.9	N/A	24-Apr-12	Anchor Bay Entertianment	Brittania Nicol, Henry Garrett, James Mapes, Lesley Mackie	2,155	https://images-na.ssl-images-amazon.com/images/M/MV5BMTkyNzkyODE5N15BMl5BanBnXkFtZTcwNjUxNzIxNw@@._V1_SX300.jpg	Robin Hardy	27-Jan-12	96 min	Drama, Horror	N/A	7750000	0	Winter	1243900000	0.36	58	21446552	88	14100000	sex-scene\|female-nudity\|folk-horror\|british-horror\|supernatural-horror\|three-word-title\|plant-in-title\|satire\|black-comedy\|second-part\|sequel
tt0326965	In My Sleep	Marcus is a popular massage therapist who struggles with parasomnia, a severe sleepwalking disorder that causes him to do things in his sleep that he cannot remember the next day. When he …	PG-13	5.6	33	1-Oct-10	Morning Star Pictures	Philip Winchester, Tim Draxl, Lacey Chabert, Abigail Spencer	1,741	https://images-na.ssl-images-amazon.com/images/M/MV5BNzg1MDM1NzIwMV5BMl5BanBnXkFtZTcwNzMxMTU1MQ@@._V1_SX300.jpg	Allen Wolf	23-Apr-10	104 min	Drama, Mystery, Thriller	6 wins.	1000000	57190	Spring	1626800000	0.30	62	26238710	93	17500000	knife\|flashback\|falling-down-stairs\|policeman\|cemetery\|surprise-party\|spa\|swimming-pool\|handcuffs\|man-in-swimsuit\|beefcake\|bare-chested-male\|vegetarian\|vegan\|independent-film
tt0327597	Coraline	An adventurous girl finds another world that is a strangely idealized version of her frustrating home, but it has sinister secrets.	PG	7.7	80	21-Jul-09	Focus Features	Dakota Fanning, Teri Hatcher, Jennifer Saunders, Dawn French	159,786	https://images-na.ssl-images-amazon.com/images/M/MV5BMzQxNjM5NzkxNV5BMl5BanBnXkFtZTcwMzg5NDMwMg@@._V1_SX300.jpg	Henry Selick	6-Feb-09	100 min	Animation, Family, Fantasy	Nominated for 1 Oscar. Another 7 wins & 43 nominations.	60000000	75286229	Winter	1227100000	0.17	62	19791935	64	19200000	parallel-worlds\|stop-motion\|scissors\|new-home\|eye\|dream\|secret-door\|cat\|rescue\|talking-cat\|spiderweb\|seashell-bikini\|spiral-staircase\|scene-after-end-credits\|puppet-animation\|garment-button\|lifting-someone-into-the-air\|thunderstorm\|monster\|crying\|shadow\|loneliness\|boat\|rainbow\|blood\|orphan\|woods\|forename-as-title\|one-word-title\|bechdel-test-passed\|husband-wife-relationship\|little-girl\|moving-crew\|pet-cat\|stuffed-animal\|pet-dog\|old-woman\|thunder\|letter\|bicycling\|little-boy\|dowsing\|forest\|movers\|search\|clue\|flashlight\|fear\|riddle\|tears\|fireplace\|stage\|anger\|spotlight\|beetle\|big-top\|child-protagonist\|female-protagonist\|search-for-parent\|sleep\|void\|alternate-world\|camera\|walker\|stabbing-a-doll\|cane\|hanging-from-a-flagpole\|angel\|snow\|eccentric\|pizza\|lemonade\|stuffed-toy-dog\|moving\|swinging-on-a-door\|stuffed-animal-toy\|reflection\|motorcycle\|other-father\|tea\|catalogue\|gloves\|clothing-store\|toy-chest\|texas\|michigan\|suitcase\|rain\|hummingbird\|flowers\|breaking-mirror\|candy\|disappearance-of-one’s-father\|disappearance\|running-away\|dinner\|theatre-audience\|theatre-production\|diving-into-a-barrel\|song\|singing\|singer\|shakespearean-quotation\|reference-to-william-shakespeare\|lightning\|moving-van\|mermaid\|actress\|cheese\|balancing-on-a-balcony-railing\|balcony\|parachute\|knitting-needle\|mirror\|computer\|voice-over-narration\|wallpaper\|corset\|cell-phone\|dog\|oregon\|player-piano\|pianist\|eyeglasses\|photograph\|skipping-stone\|milkshake\|tent\|pajamas\|presidents’-day\|lorgnette\|hide-and-seek\|cake\|candle\|bedroom\|nightmare\|sleeping\|prayer\|eating\|food\|buxom\|boy\|mother-daughter-relationship\|father-daughter-relationship\|sewing\|thread\|needle\|horror-for-children\|dark-fantasy\|theatre\|blue-hair\|tunnel\|trapeze\|toy-train\|tickling\|tea-leaves\|snowglobe\|slug\|praying-mantis\|peeling-skin\|mouse\|high-dive\|garden\|fortune-telling\|fog\|dowsing-rod\|cannon\|bicycle\|bat\|poison-oak\|mirror-as-portal\|blowing-a-raspberry\|well-shaft\|rat\|old-mansion\|metamorphosis\|mechanical-hand\|insect\|grandmother-grandson-relationship\|eye-cut-out\|cat-and-mouse\|bug\|acrobat\|impostor\|talking-animal\|secret-passage\|piano\|old-dark-house\|neighbor\|kidnapping\|key\|ghost\|ghost-child\|game-playing\|fantasy-world\|doll\|cotton-candy\|circus\|surrealism\|3-dimensional\|cult-film\|stop-motion-animation\|death-of-mother\|based-on-novel\|title-spoken-by-character\|character-name-in-title\|laptop-computer
tt0337584	Backseat	A “coming of age” story where two old friends flee from New York City on a three-day road trip to Montreal, Canada to escape their problems.	N/A	7.0	32	N/A	Truly Indie	Josh Alexander, Starla Benford, William Bogert, Robert T. Bogue	69	https://images-na.ssl-images-amazon.com/images/M/MV5BMTUwMDk1ODczMl5BMl5BanBnXkFtZTcwMzU2OTc1MQ@@._V1_SX300.jpg	Bruce Van Dusen	28-Mar-08	80 min	Comedy	1 win.	12343	0	Spring	1074900000	-0.20	55	19543636	111	9700000	road-trip\|highway-travel\|road-movie\|on-the-road

Feature Evaluation

The table below indicates how all the orignal features were evaluated and modified.

Feature	Outcome	Evaluation
imdbid	Eliminated	Determined to not be meaningful for a multiple linear regression approach.
title	Eliminated	Determined to not be meaningful for a multiple linear regression approach.
plot	Eliminated	Determined to not be meaningful for a multiple linear regression approach.
rating	Cleaned	Category needed cleaning, so we collapsed in to fewer number of like categories
imdb_rating	Left As-Is	Used continuous variable without transformation
metacritic	Left As-Is	Used continuous variable without transformation
dvd_release	Eliminated	Determined to not be meaningful for a multiple linear regression approach.
production	Split & Cleaned	Kept only the first item in the comma delimited list, then collapsed in to fewer categories. We grouped companies together that were misspelled or named only slightly different.
actors	Split	Split the first and second items in a comma separated list as Lead1 and Lead2.
imdb_votes	Left As-Is	Used continuous variable without transformation
poster	Eliminated	Determined to not be meaningful for a multiple linear regression approach.
director	Split	Split the first item in a comma separated list as Director.
release_date	Eliminated	Determined to not be meaningful for a multiple linear regression approach.
runtime	Left As-Is	Used continuous variable without transformation
genre	Split	Split the first and second items in a comma separated list as genre1 and genre2.
awards	Eliminated	Determined to not be meaningful for a multiple linear regression approach.
keywords	Eliminated	Determined to not be meaningful for a multiple linear regression approach.
Budget	Left As-Is	Used continuous variable without transformation
box office gross	Left As-Is	Used continuous variable without transformation
Box Office Season	Left As-Is	Used continuous variable without transformation
Season Gross	Left As-Is	Used continuous variable without transformation
Season YoY	Left As-Is	Used continuous variable without transformation
Season Days	Left As-Is	Used continuous variable without transformation
Season Daily Avg	Left As-Is	Used continuous variable without transformation
Season Movie Count	Left As-Is	Used continuous variable without transformation
Season Move Avg Gross	Left As-Is	Used continuous variable without transformation
Year	Left As-Is	Used continuous variable without transformation

Observation Evaluation

Our client asked us to focus strictly on their live-action, feature films that were released in the US over the last 5 years. Therefore, we removed observations with the following attributes:
- International Movies: Movies from production companies outside the US were removed, and were not factored in to our exploratory data analysis.
- Genre filtering: Movies with genre1 of ‘Animation’, or ‘Documentary’ were filtered out at client’s request.
- Release Date filtering: Movies prior to July of 2012 were filtered out at the client’s request.
- Runtime filtering: Only movies with a runtime of 80 minutes or longer are officially recognized as feature films. Therefore, due to client’s requirements, and film with a runtime less that 80 minutes was eliminated.

Missing Data Remediation

Once we had filtered out observations that were not to be used we still had some missing values that need to be dealt with. Here is how we handled those features with missing values:
- Budget & Box Office Gross: Any movie that had been released but budget and/or box office gross total could not be obtained were eliminated from the dataset. We did not feel these values could be reliably imputed due to vast variance in these numbers.
- IMDB rating, IMDB votes, &Metacritic Score: These values were fairly normally distributed so we imputed missing values by using the feature’s median value.

Feature Engineering

At VARS Consulting, our domain knowledge allows us to create meaningful features using source data to enhance the model input data and provide the best possible results. We engineered, or added, several features based on proprietary criteria to enable very high cardinality categorical data such as Production Company, Director, & Actors to provide meaning. This is especially needed because past success for Directors and Actors can heavily influence future movie performance. Our methodology was as follows:
Box Office Performance Points
>Each movie was ranked according to lifetime box office performance. We then identify movies that were ranked 1-10 as Top 10 movies, movies ranked 11-50 as Top 50 movies, and movies ranked 51-250 as Top 250 movies. Each Production, Director and Actor in the data set was then awarded 250 performance points for each movie in the Top 10, 50 performance points for each movie in the Top 50, and 10 performance points for each movie in the Top 250.
[Performance Points] = [ SUM(Top 10 Count) x 250 ] + [ SUM(Top 50 Count) x 50 ] + [ SUM(Top 250 Count) x 10 ]

An example, for Directors, shows high ranking directors according to the formula and gives us a meaningful continuous variable to assist with modeling:

Director	Sum.of.Top.10	Sum.of.Top.50	Sum.of.Top.250	Points
Christopher Nolan	2	1	2	570
Joss Whedon	2	0	0	500
Bill Condon	1	2	0	350
J.J. Abrams	1	0	3	280
Gareth Edwards	1	0	1	260
Andrew Stanton	1	0	0	250
Colin Trevorrow	1	0	0	250
James Cameron	1	0	0	250
Francis Lawrence	0	3	0	150
Jon Favreau	0	3	0	150
Michael Bay	0	2	2	120
David Yates	0	2	1	110
Zack Snyder	0	2	1	110
James Gunn	0	2	0	100
Clint Eastwood	0	1	2	70
Peter Jackson	0	1	2	70
Todd Phillips	0	1	2	70
Anthony Russo	0	1	1	60
Byron Howard	0	1	1	60
Chris Renaud	0	1	1	60
James Wan	0	1	1	60
Kyle Balda	0	1	1	60
Pierre Coffin	0	1	1	60
Steven Spielberg	0	1	1	60

Importing The Data

Finally, we brought our cleaned and prepared dataset in to R to begin data analysis and model building.

Box.Office.Gross	Season.Gross	Season.YoY.Change	Season.Days	Season.Daily.Avg	Season.Movie.Count	Season.Movie.Avg	Budget	runtime	imdb_rating	imdb_votes	metacritic	Director.Perf.Pts	Rating.Genre.Perf.Pts	Box.Office.Season	rating.group	genre1
31537320	1397500000	-0.059	55	25409091	113	12400000	1e+06	83	5.6	50796	59	0	0	Spring	R	Drama
64473115	4851100000	0.127	122	39763115	232	20900000	3e+06	85	5.7	155490	41	0	0	Summer	R	Horror
35385560	1117700000	0.017	62	18027419	103	10900000	4e+06	91	4.6	30304	30	0	10	Winter	R	Mystery
2184640	1277200000	-0.161	58	22020690	133	9600000	5e+06	118	4.1	5359	42	10	60	Fall	PG	Adventure
65206105	1277200000	-0.161	58	22020690	133	9600000	5e+06	94	6.2	82263	55	20	10	Fall	PG-13	Horror
50856010	1522300000	0.325	65	23420000	159	9600000	5e+06	89	4.4	37506	38	0	10	Fall	PG-13	Horror

Exploring The Data

Exploratory data analysis is an approach that utilizes various techniques to detect any mistakes, check underlying assumptions and roughly determine the relationship among the explanatory variables. Some EDA techniques are graphical in nature whereas some are quantitative.

Depending on the type of data that has to be explored, the exploratory data analysis can be of the following:

Univariate Non-graphical
Multivariate Non-graphical
Univariate Graphical
Multivariate Graphical

We checked some box-plots as they show robust measures of location and spread along with information about symmetry and outliers. Similarly histograms were reviewed as they quickly depict the central tendency and modality of the data.

In case of our client, we considered certain numerical values for conducting exploratory data analysis. The run time of the movies, number of votes on IMDb in last 5 years and the available budget of every movie was studied from its graphical nature. Here are some of our findings:

In addition, both the season the movie is released and the rating given by the MPAA can have a significant impact on the box office performance as seen in these graphs:

The combination of rating, and season also creates significant variation in performance:

As per the EDA we observed that the data was skewed for certain parameters, and needed smoothing. We cannot always rely on data uploaded by the source and therefore, we had to make some modifications and clean the data to make it relevant for superior analysis.

Multiple Linear Regression - Initial Assessment

At first, we simply build a model that utilizes all data to evaluate the potential of a linear model for the client:

bo <- lm(Box.Office.Gross ~ .
         ,data = all_vars)
summary(bo)

## 
## Call:
## lm(formula = Box.Office.Gross ~ ., data = all_vars)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -60239091 -16845344         0  18832919  64086533 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)   
## (Intercept)              -2.304e+08  3.563e+08  -0.647  0.52229   
## Season.Gross             -1.151e-01  8.783e-02  -1.310  0.19926   
## Season.YoY.Change        -1.007e+06  7.604e+07  -0.013  0.98951   
## Season.Days               1.844e+06  4.938e+06   0.374  0.71114   
## Season.Daily.Avg          1.099e+00  9.605e+00   0.114  0.90961   
## Season.Movie.Count        1.049e+06  2.078e+06   0.505  0.61713   
## Season.Movie.Avg          6.840e+00  2.059e+01   0.332  0.74190   
## Budget                    4.764e-01  2.618e-01   1.820  0.07791 . 
## runtime                   5.359e+05  6.344e+05   0.845  0.40434   
## imdb_rating               5.441e+06  1.236e+07   0.440  0.66266   
## imdb_votes                6.128e+01  8.942e+01   0.685  0.49795   
## metacritic                3.425e+05  6.344e+05   0.540  0.59290   
## Director.Perf.Pts         1.236e+06  7.323e+05   1.688  0.10085   
## Lead1.Perf.Points         8.152e+05  4.478e+05   1.821  0.07776 . 
## Lead2.Perf.Points        -6.930e+04  4.283e+05  -0.162  0.87246   
## Rating.Genre.Perf.Pts    -3.369e+04  9.975e+03  -3.378  0.00189 **
## Box.Office.SeasonHoliday  7.215e+07  1.483e+08   0.487  0.62980   
## Box.Office.SeasonSpring   7.077e+07  3.318e+07   2.133  0.04045 * 
## Box.Office.SeasonSummer   9.416e+07  2.290e+08   0.411  0.68365   
## Box.Office.SeasonWinter   4.336e+07  5.122e+07   0.846  0.40340   
## rating.groupPG-13        -5.887e+07  7.615e+07  -0.773  0.44496   
## rating.groupR            -5.837e+07  7.395e+07  -0.789  0.43554   
## genre1Adventure          -6.989e+07  4.662e+07  -1.499  0.14331   
## genre1Biography          -4.037e+07  3.266e+07  -1.236  0.22528   
## genre1Comedy             -7.419e+06  1.961e+07  -0.378  0.70758   
## genre1Crime              -4.551e+07  2.931e+07  -1.553  0.13004   
## genre1Drama              -1.239e+07  2.790e+07  -0.444  0.65983   
## genre1Horror              3.977e+07  2.717e+07   1.464  0.15272   
## genre1Mystery             5.218e+06  4.768e+07   0.109  0.91351   
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 38920000 on 33 degrees of freedom
## Multiple R-squared:  0.9137, Adjusted R-squared:  0.8404 
## F-statistic: 12.47 on 28 and 33 DF,  p-value: 8.405e-11

par(mfrow = c(2, 2))
plot(bo)

Multiple Linear Regression - Best Subset

The initial look makes us believe we have a data structure conducive to linear regression, but we need to find the simplest combination of dependent variables that still produces acceptable results. To do this we employ a best subset approach:

# BEGIN best subset approach
#

best.subset <- regsubsets(Box.Office.Gross~., all_vars, nvmax = 30, nbest = 10, really.big = T)
best.subset.summary <- summary(best.subset)

# Show plots evaluating the results of best subset approach
par(mfrow=c(2,2))
plot(best.subset$rss, xlab="Number of Variables", ylab="RSS", type="l")
plot(best.subset.summary$adjr2, xlab="Model Index Number", ylab="Adjusted RSq", type="l")
plot(best.subset.summary$cp, xlab="Model Index Number", ylab="CP", type="l")
plot(best.subset.summary$bic, xlab="Model Index Number", ylab="BIC", type="l")

In addition to R-squared, Adjusted R-squared, C_p, & BIC values we need to understand VIF and Durbin Watson values of each prospective model to make the best possible selection. VARS Consulting adds these values to the best subset data frame as follows:

bt <- best.subset.summary$which
best.subset.tests <- data.frame(vif=double(),dwtval=double(),dwpval=double())
for (i in 1:length(bt[,2])) {
  loop_df <- all_vars
  for (j in 1:13) {
    if (bt[i,j] == FALSE) {
      loop_df <- loop_df[,!names(loop_df) %in% colnames(bt)[j]]
      #print(colnames(bt)[j])
    } #else {print("It's false")}
  }
  vif_val <- -999
  dwt_val <- -999
  dwp_val <- -999
  tryCatch({
    vif_val <- max(vif(lm(Box.Office.Gross ~.,data = loop_df))[,3])
    dwt_val <- durbinWatsonTest(lm(Box.Office.Gross ~.,data = loop_df))$dw
    dwp_val <- durbinWatsonTest(lm(Box.Office.Gross ~.,data = loop_df))$p
  }, error=function(e){})
  best.subset.tests[i,1] <- vif_val
  best.subset.tests[i,2] <- dwt_val
  best.subset.tests[i,3] <- dwp_val
}


all_results <- data.frame(best.subset.summary$rsq,best.subset.summary$adjr2,best.subset.summary$cp,best.subset.summary$bic,best.subset.tests)

Finally, we filter the data frame to find the prospective model that meets all of our criteria thresholds:

# Filter data frame to find models that meet all criteria
all_results[all_results$vif < 5 & all_results$vif > 0 & all_results$best.subset.summary.rsq > .7 & all_results$best.subset.summary.adjr2 > 0.7 & all_results$dwtval > 1.95 & all_results$dwtval < 2.05,] #& all_results$dwtval > 2.00

##    best.subset.summary.rsq best.subset.summary.adjr2
## 82               0.8777332                 0.8565717
## 89               0.8739507                 0.8521345
##    best.subset.summary.cp best.subset.summary.bic      vif   dwtval dwpval
## 82               4.737516               -89.02476 4.928035 2.029804  0.828
## 89               6.183427               -87.13574 4.610032 2.032820  0.836

# Show variables of selected model
best.subset.summary$which[82,]

##              (Intercept)             Season.Gross        Season.YoY.Change 
##                     TRUE                    FALSE                    FALSE 
##              Season.Days         Season.Daily.Avg       Season.Movie.Count 
##                    FALSE                     TRUE                    FALSE 
##         Season.Movie.Avg                   Budget                  runtime 
##                    FALSE                     TRUE                    FALSE 
##              imdb_rating               imdb_votes               metacritic 
##                    FALSE                    FALSE                    FALSE 
##        Director.Perf.Pts        Lead1.Perf.Points        Lead2.Perf.Points 
##                     TRUE                     TRUE                    FALSE 
##    Rating.Genre.Perf.Pts Box.Office.SeasonHoliday  Box.Office.SeasonSpring 
##                     TRUE                     TRUE                     TRUE 
##  Box.Office.SeasonSummer  Box.Office.SeasonWinter        rating.groupPG-13 
##                     TRUE                    FALSE                    FALSE 
##            rating.groupR          genre1Adventure          genre1Biography 
##                    FALSE                    FALSE                    FALSE 
##             genre1Comedy              genre1Crime              genre1Drama 
##                    FALSE                    FALSE                    FALSE 
##             genre1Horror            genre1Mystery 
##                     TRUE                    FALSE

Multiple Regression - Final Model Selection

The model chosen, based on our proprietary best subset approach tells us that the simplest model that performs best includes:
- Season Daily Average
- Budget
- Director Performance Points
- Lead Actor 1 Performance Points
- Rating Genre Performance Points
- Box Office Season
- Genre 1

This is good confirmation that VARS Consulting feature engineering efforts were of significant value to the final model.

bo4 <- lm(Box.Office.Gross ~
            Season.Daily.Avg
            + Budget
            + Director.Perf.Pts
            + Lead1.Perf.Points
            + Rating.Genre.Perf.Pts
            + Box.Office.Season
            + genre1
            ,data = all_vars)

summary(bo4)

## 
## Call:
## lm(formula = Box.Office.Gross ~ Season.Daily.Avg + Budget + Director.Perf.Pts + 
##     Lead1.Perf.Points + Rating.Genre.Perf.Pts + Box.Office.Season + 
##     genre1, data = all_vars)
## 
## Residuals:
##       Min        1Q    Median        3Q       Max 
## -92277096 -15242764  -4034985  18327847  73913164 
## 
## Coefficients:
##                            Estimate Std. Error t value Pr(>|t|)    
## (Intercept)               1.552e+08  5.301e+07   2.927 0.005346 ** 
## Season.Daily.Avg         -6.046e+00  2.314e+00  -2.613 0.012154 *  
## Budget                    4.714e-01  1.678e-01   2.810 0.007309 ** 
## Director.Perf.Pts         1.028e+06  5.261e+05   1.954 0.056929 .  
## Lead1.Perf.Points         1.033e+06  3.784e+05   2.729 0.009028 ** 
## Rating.Genre.Perf.Pts    -3.191e+04  8.196e+03  -3.894 0.000324 ***
## Box.Office.SeasonHoliday  1.501e+08  5.615e+07   2.672 0.010450 *  
## Box.Office.SeasonSpring   8.214e+07  2.451e+07   3.351 0.001637 ** 
## Box.Office.SeasonSummer   1.202e+08  3.465e+07   3.469 0.001164 ** 
## Box.Office.SeasonWinter   7.917e+06  1.809e+07   0.438 0.663766    
## genre1Adventure          -4.951e+07  2.932e+07  -1.688 0.098248 .  
## genre1Biography          -1.046e+07  2.123e+07  -0.493 0.624710    
## genre1Comedy             -2.789e+06  1.589e+07  -0.176 0.861431    
## genre1Crime              -3.805e+07  2.233e+07  -1.704 0.095233 .  
## genre1Drama              -2.419e+07  2.260e+07  -1.070 0.290135    
## genre1Horror              3.516e+07  2.132e+07   1.649 0.106040    
## genre1Mystery            -2.027e+07  4.014e+07  -0.505 0.616040    
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
## 
## Residual standard error: 36940000 on 45 degrees of freedom
## Multiple R-squared:  0.8939, Adjusted R-squared:  0.8562 
## F-statistic:  23.7 on 16 and 45 DF,  p-value: < 2.2e-16

par(mfrow = c(2, 2))
plot(bo4)

vif(bo4)

##                            GVIF Df GVIF^(1/(2*Df))
## Season.Daily.Avg      22.273033  1        4.719431
## Budget                 3.974359  1        1.993579
## Director.Perf.Pts     13.203012  1        3.633595
## Lead1.Perf.Points     14.529188  1        3.811717
## Rating.Genre.Perf.Pts  2.649588  1        1.627756
## Box.Office.Season     38.563123  4        1.578598
## genre1                 4.034130  7        1.104760

durbinWatsonTest(bo4)

##  lag Autocorrelation D-W Statistic p-value
##    1     -0.01069427       2.00018   0.668
##  Alternative hypothesis: rho != 0

Finally, we plot the resulting model to evaluate how close our predictions are to actual data:

par(mfrow = c(1, 1))
plot(predict(bo4),all_vars$Box.Office.Gross,
     xlab="Predicted Box Office Gross $",ylab="Actual Box Office Gross $")
abline(a=0,b=1)

Predicting Future Performance

Based on the best model we have made predictions for the Box office gross. Here is the data for the client’s upcoming theatrical releases:

Box.Office.Gross
Season.Gross
Season.YoY.Change
Season.Days
Season.Daily.Avg
Season.Movie.Count
Season.Movie.Avg
Budget
runtime
imdb_rating
imdb_votes
metacritic
Director.Perf.Pts
Lead1.Perf.Points
Lead2.Perf.Points
Rating.Genre.Perf.Pts
Box.Office.Season
rating.group
genre1

Season.Gross	Season.YoY.Change	Season.Days	Season.Daily.Avg	Season.Movie.Count	Season.Movie.Avg	runtime	imdb_rating	imdb_votes	metacritic	Lead1.Perf.Points	Rating.Genre.Perf.Pts	Box.Office.Season	rating.group	genre1
NA	-0.006	58	19.6	96	11.9	105	6.3	14496	53	0	2570	Winter	PG-13	Action
NA	-0.152	122	31.0	245	15.4	105	6.3	14496	53	0	60	Summer	R	Horror
NA	0.103	58	20.8	157	7.7	105	6.3	14496	53	0	40	Fall	PG-13	Comedy
NA	-0.672	59	16.0	64	14.8	105	6.3	14496	53	10	40	Holiday	R	Adventure

Finally, we predict future box office revenue using our model:

predict(bo4,feat)

##         1         2         3         4 
##  81059502 308588176 151097635 264754577

BANA 6610: Final Report